0%

[Leetcode]313. Super Ugly Number(C++)

题目描述

题目链接:313. Super Ugly Number

A super ugly number is a positive integer whose prime factors are in the array primes.

Given an integer n and an array of integers primes, return the nth super ugly number.

The nth super ugly number is guaranteed to fit in a 32-bit signed integer.

例子

例子 1

Input: n = 12, primes = [2,7,13,19]
Output: 32
Explanation: [1,2,4,7,8,13,14,16,19,26,28,32] is the sequence of the first 12 super ugly numbers given primes = [2,7,13,19].

例子 2

Input: n = 1, primes = [2,3,5]
Output: 1
Explanation:1 has no prime factors, therefore all of its prime factors are in the array primes = [2,3,5].

Constraints

  • 1 <= n <= 10^6
  • 1 <= primes.length <= 100
  • 2 <= primes[i] <= 1000
  • primes[i] is guaranteed to be a prime number.
  • `All the values of primes are unique and sorted in ascending order.

解题思路

这一题有一个比较简单的思路(非最优解),创建一个小顶堆(优先队列)和哈希表,哈希表存储小顶堆中存储过的元素,首先将所有质数和 1 压入小顶堆中(以及哈希表),每次弹出一个最小值,并和所有质数相乘,保证为超级丑数。如果该数没出现过则压入优先队列中,由于每次弹出的都是超级丑数(并且大小一定是递增的),因此第 n 个弹出的数即为结果。代码如下:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
#include <limits.h>
#include <queue>
#include <unordered_set>
#include <vector>

class Solution {
public:
int nthSuperUglyNumber(int n, std::vector<int>& primes) {
if (n == 1) {
return 1; // the first super ugly number
}

int count = 0;
std::priority_queue<int, std::vector<int>, std::greater<int>> pq;
std::unordered_set<int> hset;

pq.push(1);
hset.insert(1);
for (auto prime : primes) {
pq.push(prime);
hset.insert(prime);
}

int num = 1;
while (count < n) {
num = pq.top();
pq.pop();
for (auto prime : primes) {
long new_ugly_num = num * prime;
if (new_ugly_num <= INT_MAX && hset.count(new_ugly_num) == 0) {
hset.insert(new_ugly_num);
pq.push(new_ugly_num);
}
}
count++;
}

return num;
}
};
  • 时间复杂度: O(nklog(n))
  • 空间复杂度: O(n)

GitHub 代码同步地址: 313.SuperUglyNumber.cpp

其他题目:
GitHub: Leetcode-C++-Solution
博客: Leetcode-Solutions